Rolling Excess Kurtosis (KURTOSIS)

Summary

An estimate, from the trailing window, of the excess kurtosis of the distribution its values come from: the fourth standardised moment minus 3, so a normal distribution reads 0. A tail-weight measure: above 0 the distribution has heavier tails than a normal one with the same variance, below 0 lighter ones. The companion to the shipped VAR and STDDEV in the same group.

Chart

Reference data (CSV) · Chart (SVG)

Chart metadata i

Outputs

• outReal: line · zero · positive · negative

Formula

Sample-adjusted Fisher excess kurtosis, the estimator usually written G2. With window size n, window mean x̄, and sample variance s² = Σ(x−x̄)²/(n−1):

G2 = [ n(n+1) / ((n−1)(n−2)(n−3)) ] · [ Σ(x−x̄)⁴ / s⁴ ]  −  3(n−1)² / ((n−2)(n−3))

The result is NaN when s² = 0, that is when every value in the window is equal.

optInTimePeriod must be at least 4: the (n−2)(n−3) denominators are undefined below it. The bound is enforced by the parameter range, so a shorter period is refused rather than silently degraded.

Notes

• This is G2, the form Excel KURT and scipy.stats.kurtosis(bias=False) compute. The other form in circulation is the biased g2 = m₄/m₂² − 3 over population moments, a different estimator rather than a rounding convention: G2 = (n−1)((n+1)·g2 + 6) / ((n−2)(n−3)).
• A point mass has no defensible excess kurtosis, so the degenerate window is NaN rather than a number: 0 would assert normality and −1.2 uniformity. This is deliberately unlike VAR, which floors to zero — a variance of zero says something true about the window.
• The result is at most n, the value of one reading apart from n−1 equal ones, so a window dominated by one outlier is legitimately far above 0.

Inputs

• inReal — The series to measure

Outputs

• outReal — Excess kurtosis of the trailing window, or NaN where the window has no spread

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	30	4–10000	Number of trailing values in the window

Properties

Numerical Stability: Start-Independent

☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Display Shift

✅ Can Output NaN or ±Inf i
☐ Identity at Period 1
☐ Uses Transcendental
☐ Input Must Be Positive

Example

C

#include <stdio.h>
#include <ta_libc.h>

int n = 252;
double series[252]; /* your data, oldest first */
double out[252];
int outBegIdx, outNBElement;

TA_Initialize();
TA_KURTOSIS( 0, n - 1, series, 30, &outBegIdx, &outNBElement, out );
printf( "%d values from bar %d; last out = %f\n", outNBElement, outBegIdx, out[outNBElement - 1] );

Rust

use ta_lib::Core;

let series = vec![0.0; 252]; // your data, oldest first
let mut out = vec![0.0; 252];

let core = Core::new();
let range = core.kurtosis(0, series.len() - 1, &series, 30, &mut out)?;
println!("{} values from bar {}; last out = {}", range.count, range.beg_idx, out[range.count - 1]);

Java

import io.github.talib.Core;
import io.github.talib.OutRange;

double[] series = new double[252]; // your data, oldest first
double[] out = new double[252];

Core core = Core.DEFAULT;
OutRange r = core.kurtosis(0, series.length - 1, series, 30, out);
System.out.println(r.count() + " values from bar " + r.begIdx() + "; last out = " + out[r.count() - 1]);

C#

using System;
using TALib;

var series = new double[252]; // your data, oldest first
var outReal = new double[252];

var core = Core.Default;
OutRange r = core.Kurtosis(0, series.Length - 1, series, 30, outReal);
Console.WriteLine($"{r.Count} values from bar {r.BegIdx}; last outReal = {outReal[r.Count - 1]}");

TypeScript

import { kurtosis } from 'ta-lib';

const series = new Float64Array(252); // your data, oldest first

const { begIdx, values } = kurtosis(series, { timePeriod: 30 });
console.log(values.length + ' values from bar ' + begIdx + '; last values = ' + values[values.length - 1]);

Implementation

Added in 0.8.3 (ta-lib-python 0.8.3).

TA-Lib Definition: kurtosis.c · kurtosis.yaml

Native	File
C	ta_KURTOSIS.c
Rust	kurtosis.rs
Java	Core_KURTOSIS.java
C#	Core_KURTOSIS.cs
TypeScript	kurtosis.ts

Python: talib.KURTOSIS (ta-lib-python 0.8.3 or later), see ta-lib-python.

TA-Lib is also available for R and more using a wrapper.

Aliases

Excess Kurtosis, Sample Excess Kurtosis, KURT

See Also

VAR · STDDEV · BBANDS

References

• Joanes, D. N. and Gill, C. A. "Comparing measures of sample skewness and kurtosis." Journal of the Royal Statistical Society: Series D, 47(1), 1998, 183-189 — the g1/g2, G1/G2, b1/b2 families and which is unbiased under which assumption.
• NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.11 — the biased population form.
• Microsoft, KURT function — the G2 form, and #DIV/0! for fewer than four points or zero standard deviation.